Asking for advice on Hessian eigenvalues warning + seasonality detrending and imputation

[PatrickPata]

Hi Jim and DSEM team,

I am wondering if you can help me understand how to adequately parameterize my DSEM models. I have two questions, which are numbered below.

For context, the data I am analyzing is a 40-year monthly monitoring of a lake as a time series of water properties, phytoplankton, zooplankton, and fish. It has many multi-year data gaps that are not consistent across variables, so I thought that the DSEM would be a good tool to have the imputation built in. I am mostly interested in testing if the ammonium and phosphate excretion by zooplankton has an effect on the phytoplankton trends.

1: After following the example scripts for the "Multi-causal ecosystem synthesis" of the Bering Sea dataset, I managed to run a simple version of my food web model (10 variables, 31 paths). However, what I am hoping for is to test a model with more variables and paths. Sometimes, when I try to increase the number of variables or increase the number of lags in the model, I get the warning: "The ratio of maximum and minimum Hessian eigenvalues is high. Some parameters might not be identifiable." I think that this could be a model convergence issue, but I am wondering if you have any advice on how to systematically resolve this warning.

2: On a different note, does the DSEM package have a built-in way to account for seasonality trends? Currently, I am running my DSEM model using a detrended data after applying the decomposition from the stlplus R package. In this process, I impute the missing values, just so the decomposition works, and then I remove the points that were imputed. So effectively, the final imputation of the detrended data happens in DSEM still. Does this seem like a reasonable approach?

Thank you in advance for looking into these questions.

[James-Thorson-NOAA]

thanks for reaching out. I'll also ping collaborators who are working on similar topics to chime in.

1. You can check fit$sdrep and if all of the SEs look reasonable, then it maybe isn't an issue. But in general, you might also try rescaling all variables to have similar scales
2. You could switch to tinyVAST, which allows you to include a formula (e.g., a fixed effect for each season) to de-season the model while fitting a DSEM; however, tinyVAST doesn't include the family = "fixed" option, so it's not a perfect swap-in replacement. Or doing two-stage like you're doing sounds reasonable ... however, it will not fully propagate uncertainty. Finally, you could include season indicators as additional variables, and estimate their impact on each other variable to estimate the season terms jointly, but that seems a bit cumbersome in terms of interface.

[PatrickPata]

Thank you so much! Your advise about rescaling and checking the standard errors. I will try and explore tinyVast.